In this paper, we study norm almost periodic measures on locally compact Abelian groups. First, we show that the norm almost periodicity of $\mu$ is equivalent to the equi-Bohr almost periodicity of $\mu*g$ for all $g$ in a fixed family of functions. Then, we show that, for absolutely continuous measures, norm almost periodicity is equivalent to the Stepanov almost periodicity of the Radon--Nikodym density.

中文翻译：

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在规范几乎定期的措施

在本文中，我们研究了局部紧阿贝尔群的范数几乎周期测度。首先，我们证明，对于固定函数族中的所有 $g$，$\mu$ 的范数几乎周期性等价于 $\mu*g$ 的等玻尔几乎周期性。然后，我们证明，对于绝对连续的度量，范数几乎周期性等价于氡-尼科迪姆密度的斯捷潘诺夫几乎周期性。